Three-state conical intersection optimization methods: development and implementation at QM/MM level

Two-state conical intersection optimization methods at both QM and QM/MM levels have been extensively implemented in many commercial and noncommercial packages in the past decade. In contrast, three-state conical intersection optimization methods are less concerned, in particular the QM/MM-based ones. In this work, we have developed a penalty function-based three-state conical intersection optimization approach in the framework of the QM/MM method. We first present the fundamental formulation of this approach, and its algorithm and implementation in our package; then, we have carried out several pilot applications on molecular systems in vacuo and aqueous solution to demonstrate the efficiency of our implemented method. Our current developments enable efficient determination of three-state conical intersection structures of molecules in solution and biological systems, which is at the heart of understanding the photophysical and photochemical mechanisms of large systems at the atomistic level.